The name George has been the favourite of bookies and Royal pundits for the last few days, with the Duke of Cambridge playing down speculation even as the couple left hospital yesterday. It is one of the Prince of Wales' middle names.

Alexander was one of the other favourite names suggested in recent days, while Louis is one of the Duke of Cambridge's own middle names and also references Earl Mountbatten, the great uncle of the Prince of Wales. Alexandra is one of the Queen's middle names.

The baby will in time become King George VII, following a tradition dating back to German-born George I, the first Hanoverian king of Great Britain who acceded to the throne in 1714.

The last was the Queen's father George VI who died in 1952 but was known to his family as Bertie.

Among the previous monarchs to have had the name, is George III - on the throne from 1760 to 1820 - who is predominantly remembered for losing the American colonies and his sanity. However, the Prince of Wales disclosed last year that he is the king he most respects, describing him as a good man who was simply misunderstood.

George was the most popular name with the bookies with betting firms William Hill, Coral and Paddy Power all offering short odds on the moniker.

While the name will be hailed for honouring members of the Royal family, it does not appear to have immediate links to the Middleton family, with neither the Duchess' father Michael or brother James included.

Swaddled in white, the baby lay in the arms of his proudly beaming mother; at her side, beaming just as proudly, his father (Warren Allott)

When asked whether he intended to call his first child George yesterday, the Duke of Cambridge smiled and replied: “Wait and see, wait and see.”

Such delays have almost become a part of royal tradition, with the public often left guessing for several days.

When the Duke was born in 1982, his parents waited a week before announcing his name, amid speculation that the Princess of Wales liked Sebastian and Oliver while her husband was hoping to call him Albert.

The Prince of Wales was christened Charles Philip Arthur George, while the Duke of Cambridge is called William Arthur Philip Louis.

The bookmakers’ favourite for the new Prince had been George for the days preceding the birth, closely followed by James. Both names, with six kings called George and two called James, were be considered suitably regal and traditional. Henry, which is Prince Harry’s official name, was also in the running, but lost out in the end to Alexander and Louis.

The proud parents leave the hospital with the as-yet unnamed baby Photo: AFP/GETTY

Charles Kidd, the editor of Debrett’s Peerage and Baronetage, predicted that the young couple would select a conventional first name.

“I do think that Prince William is quite a traditionalist – that’s my feeling,” he said.

“The fact that he chose to use the royal dukedom (of Cambridge) and has followed royal precedent, I wouldn’t be surprised if they use a name that is already familiar in the Royal family – something that has royal associations.”

The Royal baby is shown the the media outside the Lindo Wing of St Mary's Hospital (Reuters)

Midway through her pregnancy, the Duchess disclosed that she had several options for names and that her friends were giving her ideas.

“We have a shortlist for both (boy and girl) but it’s very difficult. My friends keep texting me names,” she said.

According to babycentre.co.uk, the most popular boys’ names for the first half of 2013 were Oliver, Jack, Charlie, Harry and Oscar. George was the ninth favourite and James was 10th.

One thing that is certain is that the baby will become HRH Prince (forename) of Cambridge. Justine Roberts, co-founder of Mumsnet, said it was hard to imagine the young members of the Royal family bucking the trend and “going left field” when choosing a name.

“Baby naming can often be a source of conflict for couples, and that’s without international media speculation or royal protocols to contend with,” she added.

“The advice from Mumsnet is to listen diligently to suggestions from family, nod and smile sweetly, and then politely remind them exactly who’s given birth to this child.”

The Middletons were the future king’s first visitors yesterday. When Mrs Middleton was asked as she left the hospital whether she had suggested a name, she laughed and said: “Absolutely not.”